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Journal of Operator Theory

Volume 71, Issue 1, Winter 2014  pp. 3-13.

Infinite multiplicity of abelian subalgebras in free group subfactors

Authors Marius B. Stefan
Author institution: Waltham, MA 02453, U.S.A.

Summary:  We obtain an estimate of Voiculescu's (modified) free entropy dimension for generators of a II$_1$-factor $\mathcal{M}$ with a subfactor $\mathcal{N}$ containing an abelian subalgebra $\mathcal{A}$ of finite multiplicity. It implies in particular that the interpolated free group subfactors of finite Jones index do not have abelian subalgebras of finite multiplicity or Cartan subalgebras.

Keywords:  free group factors, free entropy

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